{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Deep Learning Models -- A collection of various deep learning architectures, models, and tips for TensorFlow and PyTorch in Jupyter Notebooks.\n",
    "- Author: Sebastian Raschka\n",
    "- GitHub Repository: https://github.com/rasbt/deeplearning-models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sebastian Raschka \n",
      "\n",
      "CPython 3.7.1\n",
      "IPython 7.2.0\n",
      "\n",
      "torch 1.0.0\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -a 'Sebastian Raschka' -v -p torch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Runs on CPU or GPU (if available)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model Zoo -- Variational Autoencoder"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A simple variational autoencoder that compresses 768-pixel MNIST images down to a 15-pixel latent vector representation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import time\n",
    "import numpy as np\n",
    "import torch\n",
    "import torch.nn.functional as F\n",
    "from torch.utils.data import DataLoader\n",
    "from torchvision import datasets\n",
    "from torchvision import transforms\n",
    "\n",
    "\n",
    "if torch.cuda.is_available():\n",
    "    torch.backends.cudnn.deterministic = True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Device: cuda:0\n",
      "Image batch dimensions: torch.Size([128, 1, 28, 28])\n",
      "Image label dimensions: torch.Size([128])\n"
     ]
    }
   ],
   "source": [
    "##########################\n",
    "### SETTINGS\n",
    "##########################\n",
    "\n",
    "# Device\n",
    "device = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")\n",
    "print('Device:', device)\n",
    "\n",
    "# Hyperparameters\n",
    "random_seed = 0\n",
    "learning_rate = 0.001\n",
    "num_epochs = 50\n",
    "batch_size = 128\n",
    "\n",
    "# Architecture\n",
    "num_features = 784\n",
    "num_hidden_1 = 500\n",
    "num_latent = 15\n",
    "\n",
    "\n",
    "##########################\n",
    "### MNIST DATASET\n",
    "##########################\n",
    "\n",
    "# Note transforms.ToTensor() scales input images\n",
    "# to 0-1 range\n",
    "train_dataset = datasets.MNIST(root='data', \n",
    "                               train=True, \n",
    "                               transform=transforms.ToTensor(),\n",
    "                               download=True)\n",
    "\n",
    "test_dataset = datasets.MNIST(root='data', \n",
    "                              train=False, \n",
    "                              transform=transforms.ToTensor())\n",
    "\n",
    "\n",
    "train_loader = DataLoader(dataset=train_dataset, \n",
    "                          batch_size=batch_size, \n",
    "                          shuffle=True)\n",
    "\n",
    "test_loader = DataLoader(dataset=test_dataset, \n",
    "                         batch_size=batch_size, \n",
    "                         shuffle=False)\n",
    "\n",
    "# Checking the dataset\n",
    "for images, labels in train_loader:  \n",
    "    print('Image batch dimensions:', images.shape)\n",
    "    print('Image label dimensions:', labels.shape)\n",
    "    break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "##########################\n",
    "### MODEL\n",
    "##########################\n",
    "\n",
    "class VariationalAutoencoder(torch.nn.Module):\n",
    "\n",
    "    def __init__(self, num_features, num_hidden_1, num_latent):\n",
    "        super(VariationalAutoencoder, self).__init__()\n",
    "        \n",
    "        ### ENCODER\n",
    "        self.hidden_1 = torch.nn.Linear(num_features, num_hidden_1)\n",
    "        self.z_mean = torch.nn.Linear(num_hidden_1, num_latent)\n",
    "        # in the original paper (Kingma & Welling 2015, we use\n",
    "        # have a z_mean and z_var, but the problem is that\n",
    "        # the z_var can be negative, which would cause issues\n",
    "        # in the log later. Hence we assume that latent vector\n",
    "        # has a z_mean and z_log_var component, and when we need\n",
    "        # the regular variance or std_dev, we simply use \n",
    "        # an exponential function\n",
    "        self.z_log_var = torch.nn.Linear(num_hidden_1, num_latent)\n",
    "        \n",
    "        \n",
    "        ### DECODER\n",
    "        self.linear_3 = torch.nn.Linear(num_latent, num_hidden_1)\n",
    "        self.linear_4 = torch.nn.Linear(num_hidden_1, num_features)\n",
    "\n",
    "    def reparameterize(self, z_mu, z_log_var):\n",
    "        # Sample epsilon from standard normal distribution\n",
    "        eps = torch.randn(z_mu.size(0), z_mu.size(1)).to(device)\n",
    "        # note that log(x^2) = 2*log(x); hence divide by 2 to get std_dev\n",
    "        # i.e., std_dev = exp(log(std_dev^2)/2) = exp(log(var)/2)\n",
    "        z = z_mu + eps * torch.exp(z_log_var/2.) \n",
    "        return z\n",
    "        \n",
    "    def encoder(self, features):\n",
    "        x = self.hidden_1(features)\n",
    "        x = F.leaky_relu(x, negative_slope=0.0001)\n",
    "        z_mean = self.z_mean(x)\n",
    "        z_log_var = self.z_log_var(x)\n",
    "        encoded = self.reparameterize(z_mean, z_log_var)\n",
    "        return z_mean, z_log_var, encoded\n",
    "    \n",
    "    def decoder(self, encoded):\n",
    "        x = self.linear_3(encoded)\n",
    "        x = F.leaky_relu(x, negative_slope=0.0001)\n",
    "        x = self.linear_4(x)\n",
    "        decoded = torch.sigmoid(x)\n",
    "        return decoded\n",
    "\n",
    "    def forward(self, features):\n",
    "        \n",
    "        z_mean, z_log_var, encoded = self.encoder(features)\n",
    "        decoded = self.decoder(encoded)\n",
    "        \n",
    "        return z_mean, z_log_var, encoded, decoded\n",
    "\n",
    "    \n",
    "torch.manual_seed(random_seed)\n",
    "model = VariationalAutoencoder(num_features,\n",
    "                               num_hidden_1,\n",
    "                               num_latent)\n",
    "model = model.to(device)\n",
    "    \n",
    "optimizer = torch.optim.Adam(model.parameters(), lr=learning_rate)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "Epoch: 048/050 | Batch 350/469 | Cost: 13372.9746\n",
      "Epoch: 048/050 | Batch 400/469 | Cost: 12831.2305\n",
      "Epoch: 048/050 | Batch 450/469 | Cost: 12963.0156\n",
      "Epoch: 049/050 | Batch 000/469 | Cost: 12832.8057\n",
      "Epoch: 049/050 | Batch 050/469 | Cost: 12771.7109\n",
      "Epoch: 049/050 | Batch 100/469 | Cost: 13143.8457\n",
      "Epoch: 049/050 | Batch 150/469 | Cost: 12863.8740\n",
      "Epoch: 049/050 | Batch 200/469 | Cost: 12841.9248\n",
      "Epoch: 049/050 | Batch 250/469 | Cost: 13240.2529\n",
      "Epoch: 049/050 | Batch 300/469 | Cost: 12889.4521\n",
      "Epoch: 049/050 | Batch 350/469 | Cost: 13022.1709\n",
      "Epoch: 049/050 | Batch 400/469 | Cost: 12963.3125\n",
      "Epoch: 049/050 | Batch 450/469 | Cost: 12778.5381\n",
      "Epoch: 050/050 | Batch 000/469 | Cost: 12820.4805\n",
      "Epoch: 050/050 | Batch 050/469 | Cost: 12769.4893\n",
      "Epoch: 050/050 | Batch 100/469 | Cost: 12682.0566\n",
      "Epoch: 050/050 | Batch 150/469 | Cost: 13312.6172\n",
      "Epoch: 050/050 | Batch 200/469 | Cost: 13716.5430\n",
      "Epoch: 050/050 | Batch 250/469 | Cost: 12201.1973\n",
      "Epoch: 050/050 | Batch 300/469 | Cost: 13228.4199\n",
      "Epoch: 050/050 | Batch 350/469 | Cost: 12986.6201\n",
      "Epoch: 050/050 | Batch 400/469 | Cost: 13097.1562\n",
      "Epoch: 050/050 | Batch 450/469 | Cost: 13272.6777\n"
     ]
    }
   ],
   "source": [
    "start_time = time.time()\n",
    "for epoch in range(num_epochs):\n",
    "    for batch_idx, (features, targets) in enumerate(train_loader):\n",
    "        \n",
    "        # don't need labels, only the images (features)\n",
    "        features = features.view(-1, 28*28).to(device)\n",
    "\n",
    "        ### FORWARD AND BACK PROP\n",
    "        z_mean, z_log_var, encoded, decoded = model(features)\n",
    "\n",
    "        # cost = reconstruction loss + Kullback-Leibler divergence\n",
    "        kl_divergence = (0.5 * (z_mean**2 + \n",
    "                                torch.exp(z_log_var) - z_log_var - 1)).sum()\n",
    "        pixelwise_bce = F.binary_cross_entropy(decoded, features, reduction='sum')\n",
    "        cost = kl_divergence + pixelwise_bce\n",
    "        \n",
    "        optimizer.zero_grad()\n",
    "        cost.backward()\n",
    "        \n",
    "        ### UPDATE MODEL PARAMETERS\n",
    "        optimizer.step()\n",
    "        \n",
    "        ### LOGGING\n",
    "        if not batch_idx % 50:\n",
    "            print ('Epoch: %03d/%03d | Batch %03d/%03d | Cost: %.4f' \n",
    "                   %(epoch+1, num_epochs, batch_idx, \n",
    "                     len(train_loader), cost))\n",
    "            \n",
    "    print('Time elapsed: %.2f min' % ((time.time() - start_time)/60))\n",
    "    \n",
    "print('Total Training Time: %.2f min' % ((time.time() - start_time)/60))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Evaluation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reconstruction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x180 with 30 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "##########################\n",
    "### VISUALIZATION\n",
    "##########################\n",
    "\n",
    "n_images = 15\n",
    "image_width = 28\n",
    "\n",
    "fig, axes = plt.subplots(nrows=2, ncols=n_images, \n",
    "                         sharex=True, sharey=True, figsize=(20, 2.5))\n",
    "orig_images = features[:n_images]\n",
    "decoded_images = decoded[:n_images]\n",
    "\n",
    "for i in range(n_images):\n",
    "    for ax, img in zip(axes, [orig_images, decoded_images]):\n",
    "        curr_img = img[i].detach().to(torch.device('cpu'))\n",
    "        ax[i].imshow(curr_img.view((image_width, image_width)), cmap='binary')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate new images"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x180 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x180 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x180 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Cio0yMxQf1aFDB/OqFM9SCFVHfVRbW9ui9zMMQ+vzZHaj+nB7RQdLCfWBxvX1119v41KxfbrbrphqaUuRl15TU9OkSqHvq1yCMmvvv/9+Tj75ZKD13mB7kSzzAbHC1JTXns1mTVnMfX2XLl3M/vb0+HPfd8V/ZDKZRtff7ChSoWbOnGmp99/4xjeAWJlKyziV/XoudO3a1eLckll8ELW5qQK6ub9LGeO77rqrKRm5Klcxaeoao+QpRa6N2WzWsoeVxThnzhwgitnNN5utvdCcUltVgHvChAmMHz8eiNeYMAxt3GqdVTzq22+/bbbpGbv33nvb2pOv2pjKzZQeOknjNMAlYyclXL1eaZ7PP/+81QrRxY96MDc0NDB//nwgTkffe++97aiiUJK12qwg+06dOlFbW7vDbQjD0GrJ3HvvvUC8uerevTsnnngiUJyLjlu6aCePHdTn8+fPtyr2ClxO62TfEbLZrG0UdQHpE088YdWjdamxFrlSQEceeqBWV1dvN7lApU40/+rr620TkrbNlNKlVets0KBBwLZzU+NxzZo1Nhf1AE8GrCuRRI5gcgPSXg5C8gispai/lADy6KOPWtt/9KMfAdFNEpC+C3Jlb01NjT1MtYHQx0wm02S1a9mde8SbnLu5NzUUkyAIrCSC+kG3RnTu3NnGrJ4ByQu51Z+ad6tXr7YxrwSRNFBXV2f3tao2lBywsWPH2vzRWJ03b56JJHr9kiVLgEhQUcC+Po4ZM8ZK9uRbKildM8FxHMdxHKfESKUypV128s497UC1e5bnt3HjRpOgf/e73wGRpygFS7KvvMFkNe2nnnoKgGOPPdbk60JVuM095quurrbdsgLhmkrflWe0evVqS6vX75KNQ4cOZcKECUC8A0+bB5lLboLBBx98YP0qL1AF6UoJ9eV7773H7NmzgbjC8ogRIyzgfPjw4UD6+wliRUZH6Bp3gwYNauTdNTQ0mCKl42ilOFdVVaUyqaChocHulFSfaS1avXq1zUGlaE+fPt1UD1UW12s2bdpkaeuqyN1UmRKN/0wmU1DlNVliRkgt1Dhdu3atBa+r7Wkdp3ofO3fubOqZEiCSR7W5imCyxI4+vvTSS0CUKKKSC2kr56ETFVXv1jPhxRdfNEVfiR/Dhw+356HuSdWpxtKlS3nnnXcAOOywwwrU+i9HquI111xjiWhS4XTM9/LLL/Ovf/0LiBXkuro6U9tkq9akzZs3W/kLrbcHH3yw/d58j/nSOSMcx3Ecx3FKhFQrU9pZv/DCC+Y56c43xSGsXbvW0lYVf9SjRw9TpuTlScmC2BtTWYKHH36Y0aNHA/Futr2DnXM98kwmY8XD1Ga1c+7cuSxYsACI48IqKyvNxlxv8bzzztsmDRpKJ3hbSs6bb77J8uXLgW1LPpQK8u7vuOMOAKZOnWoxYPKOTj31VFNE05Jq3RzZbNbuZ7v99tuBONi5oqLCbFMyxLJly7j11lsBzH6N/e7duzcqpVBM1K5Fixbxz3/+E4jju6RIVFRU8PjjjwPYnGxoaLDCmFKCpaYuXbrUPOVkQPCXjeVCqVKyVXFvGq9btmyxGBOpcx999JGlnitWNZkU0pTKU2zlqqamplGweLK4cW77mrqWTGrH5s2bGyXDpIEwDK09uh4lqYgqGF2v6du3r8VPKeFF6059fT0vvvgiUFxlSmu9YvPuv/9+a79OjfRcWLNmjZ1UJU9nZKPUZNm46667WrHZcePGAVHs347eo9ocqd5M6b6le++91+pDKPtJFU+rqqrszdCiPn78eNtMaEI99thjQLQx0eWW6gAt8lC4B7YyDiSzLly40CbCm2++CcSXii5atMi+J/r162dyp9CG8NBDDy36YtZaFDT44Ycf2sZWwZJpyqT5MtSv9913HwBXXHEFEG3m9YBV1ubIkSPtCEJjUQtHWvtv4cKF/OQnPwEiSR3iTcVbb71l9msz9fnnn1twqGzSBur8889PTTYYxH33yiuvmGOm/tGmY+3atebEaL717t2b3/zmN0B83KJ1avbs2ZZkoDUpDSSPwyB+4Kxfv97qgOkS2c8++4xjjjkGiJ3N5KYi93ismE5PcrOnDXButffmHpoap8OGDbOfz73UOw2EYWgbXx2lJ8NGlNCk+wRramoa3XGr8Tpv3rxtnoPFYPPmzZxzzjkAPPDAA0DUj8lsRIg3jlu2bLH1Q3bsv//+9lzUuqPj3oaGBnMKtKmqqqpqMwcmnSu24ziO4zhOiZBKZUocffTRQBQspkBQIa/j8MMPtwA73frdu3dv28Xq2Ei707vvvtt270oBPeywwwp+87l21yrdsG7dOttJy3NPVvWVcqEjgz333NO+ryBEBb8m72UqFaRy3HTTTUAkV0sBUMCy0s/32muvRrVj0nAEmMlkrIaZSh0oMHnw4MEcddRRQDyu+/TpY+NT7Zc60rlz51T1odp1yy232PG42qy506dPHzsOkcK4cuVKCyaVCqL6Pccee2yqbJTq0LdvXwtQlSoq1VvhBRCXaenWrZspWELrz6hRo0zhSN6dmRbUFrWte/futjapb0444QR++MMfAjS62SBpSzJ0IfeuzfZGf0/PhQ0bNlgf5N7R1xxqs9S46667zuapQjF0W0UxyWazdsqi4y6pUOPGjbObNPr27Qs03Vea1xDXJCwWU6dOtbIxSeVTY04nVVKVBgwYYIkBmovV1dX2nNAaJLp162blIvT6Dh06tNkYdWXKcRzHcRwnD5pVpoIgGAjcAfQDssDkMAyvD4JgN+BeYE9gEXBqGIZr2rJx8iimTJnC9ddfD8SxGF//+teBSJnSGWlTwaxSb+RpDhkyxFQQpUQeeeSRBS1umc1mef7554E4CH633Xbj7LPPBuJK0fKyli1bZkF3iuWora21eCupW/L4u3TpUlKB53V1dRYQqIDfrl27mhch5UOp2vPnzzfPUF7XLrvs0sjmfIuw7SiK5fr0008tVTf3rr2f/vSn1j9q3xdffNGo8rv6fOPGjaY4alwXM45K4/TJJ5+091WxQNdddx0QFb/V/Pz9738PwIMPPmiKj+azqhar79KCvPX+/ftbhW/FYmgsNlVctLKy0vpG/ang1169epkiVwpzccuWLbzxxhtAPHYvvPBCU+i2p+7kxv0lv9beYzf3doHPPvvM4mwVq9jSwrBK7Bk8eLCN/2Rhz2L35+bNm62cgdYNqTejRo3ablkcvTfJotF6RhYaqX4PPPCArZtaY4YPH26nFVKkkve9qj+kiC9ZssQUKT0ztX6OHTvWlOX2UIl3ZIQ3AD8Pw3Ao8HXgfwZBMAz4JfB4GIaDgMe3fu44juM4jrNT0azrHobhJ8AnW/+/PgiC94Ba4CTg8K0v+xvwFPC/27Jx2jUOHjyYP/3pT0Ds8Wu33alTp+0qEPod2p0GQWCvVxxVnz59Chq70dDQYAVD5a1PnDjRPEF5UGr7gAEDGt2Avnjx4m3Ou5Ovb+pm+zQhT0Qp5uedd14jL+Lkk0/mrLPOAuL3SJkbK1eutP6X6pHJZOx903uUG8fS1qhPlLk1bdo0y4Q6/vjjATjttNOAqMxHbiZUGIYWJ6fSHboKoaamxpQplQjZfffdzcZcb7O9+1sxi5988ompNZMmTQLiInqVlZWmDMiTr6+vN2VG4/v0008HIjUxTeNU46W6urpRBqnWjGRckPog6SHra0k1Kk02fhlq/6xZs2xdUeHfgQMHtmh9XLdunakihVpXNacULzNjxgxbZ7Ru6L7SqqqqHeoT/dwhhxxiirnid4qJ+mrevHl2fUzu3YTJ+web+lmV2NHzdMCAAUWLA5NK9sEHH5gdioWaPHkyY8aMARqveZlMxhR9xY7NmDHD1mBl2yp7etCgQdan7TEnW3QOEgTBnsD+wMtA360bLcIw/CQIgnYbZUEQmCynj1rkmpOPNcn0sHrnnXdYvHgxEAdsJ9MvC0FFRYUtznpgHnHEEdts+HLR1zT4Z82axaxZs7b5no4t0xTUm0RStCaygrRXr15ttivQddKkSY1qfmkh2GOPPex3qn9XrFixzSWnhUCLwCOPPAJgd0hB/GBWssPy5cu3SSiA6HhWMr0C1zU2+/TpY6nNqgQ/btw4O1qTjcnaOe2B3nM9pCBesLVh0iK8atUqrrzySiC+XaCmpsYSQy6//HKgcRBzWtA4S9aq0cZC/bhx40b7njYMySOftJa0aA7Z+fzzz9uxmJzNHV1PkmU9dnR9biv0d7QGrlu3zir0q2zAJZdcAkSXNWsMN9U+tV19Dtum1xcbPQNefvllWz/UVoVC7LPPPtvcySfk7Kh0i9aRESNGFL10x2677WbHjqq/p00VND5Grqurs9pYt912GxC9D7pr78gjjwRiZ6+9Q3l2eKQHQbALMA34aRiG61rwcxcGQfBaEASvqYhYuVHuNpa7feA2lgvlbmO52wduY7mwM9iYZIdcwyAIOhJtpP47DMMHtn55RRAE/beqUv2BT5v62TAMJwOTAcaMGdNmF3E15y1pF6s03z/84Q8AzJw503b2SiPNd8faUhsrKiqYOHEiEFfZfeWVV0wpk4eQtDHXo7j66qvteEmBkrl3ULUVbdWHskfK0uTJk4FIjdHRUfLIaHu/J3lUBpGakFuduSUKXUttzGaz9v4r6Hz27NmmPqmcg7zjfv36mTeso8nly5ebTK2Uaykc/fv3t0QJJRj07NnT3ieN2ZbcJdmaflR7FPwZhqEdeVx66aUA3HDDDUCkMOo9kWpzwQUXmCKgdOT2VCvaaqzmlgzQWGpoaNjmjrfc17c37bWeaowtXLjQjkdaq1TkmwDTGhv196RKHHjggaba6CjsmmuuAeDEE080G1XEsWvXrvY7pI78/e9/B6I7+jQXVS4h3wD0fPoxmcCiwGu17+abbwYiBVVtlVq3ePFiK1799NNPA3FYxSmnnNLmtzDsqI1qw4gRI+wESfa8//77tsbpuS1F/I477rDC1lK5jz76aH7wgx8AcdJIoRTwZle1IOq5vwLvhWF4XeJbDwE/2Pr/HwD/bPvmOY7jOI7jpJsd2bIdCnwfeCsIgte3fu3/AP8F3BcEwf8AFgPfa58mtpwwDK1Yom6qv+eee4BI4dFOWMX05DEXioqKClMY5A1MnjyZO++8E4CLLroIwALvFixYYMqazv83bdpkdqhoqQLt0hozlYxJgdgr1MfW/K7kPW9SfAqhEoRhaKpSMrBc3pNKBCTjvnRvnfpn5MiRVi5BMSvyInv16mUBtPKshgwZYvEshS5WqlIkI0eOtPsxFfQpVaO6utpiMH79618DcPbZZ6fq/r3Wovc7rXOrtWjc6eqYAQMGcMghhwAt9+ibut+u0GisjR8/3q45kuqr5I433nij0bUqffv2tXgoqSOaf3V1dZb4Uai7W7eH1s+TTz7ZYqQUcylV7eabb+auu+4CYvW6rq7OnjeyVWVKxowZU7QYRtkzfvx4i0OVqnjFFVdYCZXc/slkMvYcPfPMM4FIdSyEAt4UO5LN9xzwZSPnyLZtTtsQhqENqjlz5gDxolFVVWWbFAXGFmOB1NGc6itNnTrVgnx/9rOfAXGbGxoabCAlj7XOP/98IJavC13FvbW0xUKUew9YVVVVQS8LrqystCw7Xco5cuRI+742STpO6NmzZ6Pj5JqamkZ30yXr2CT/D01X6y3UgqGHyZQpUyzYc+7cuUB8cfNxxx1nF/7qIVUKmWw7IxpTOk7Rx3322ccyGVvad01V2C5W//fs2dPukNQ81XH8a6+9Zlm0OpbWhgtiB1cbp549e1rdMT070jCua2trrZ6bju+0qfroo48sNEQOTm1tLWPHjgViB1bHov379y9a8oT+7rhx4+xoburUqQBMnz7dBATdWKKszGSVdwWqV1dXF61vSjP1xHEcx3EcJyWkKze5jaioqLCdqqqnTp8+HYi8FB2LyaMuBjquufjii4GopsvDDz8MREHyEFcDz2Qyths/4YQTgKiUglLny+3ooSXIq0kqOYXysOTxqWK9PpYjyZpnl112WZFb4+SLlG4dfemIfOjQoTau8/Hwi63cBEFgVehVr+7UU08FouQQHU2r7Mi7775rx4L6Oa25o0aNsnIe7V27riVUVFTYCce5554AhGiaAAAELElEQVQLwDnnnANsW4VebK9PilnSQ+2qqakxRV9JK2eddZap9/oolby6ujpVd7O6MuU4juM4jpMHZalMQazWqNyAPqYF7aQVHDh48GB+/vOfA9hHZ8cplUrTjpMGlKDz0ksvAdh9fP369WuU3NHcvCp2fFRz5Ca+9OvXzwKXFeNXLsjWUjytqKystHYrkUAnOKWAK1OO4ziO4zh5ULbKlOM4jtOYZMFZZQwrM3PFihWsWxddcLGjGZktVbIcpxzxzZTjOM5OREVFhYU9KJmgLZIKfBPl7Mz4MZ/jOI7jOE4eBJJmC/LHguAzYAOwsmB/tPX0Ytt27hGGYbO1FIIgWA/MbbdWtS0ttrHE+xDK38YdHac7g40+F9ODz8UvYSexsaznIhR4MwUQBMFrYRiOKegfbQWtbWep2Aflb2M+7XQb00O5j1Mofxt9nLbfzxaSch+n0Pq2+jGf4ziO4zhOHvhmynEcx3EcJw+KsZmaXIS/2Rpa285SsQ/K38Z82uk2podyH6dQ/jb6OG2/ny0k5T5OoZVtLXjMlOM4juM4Tjnhx3yO4ziO4zh5ULDNVBAExwZBMDcIggVBEPyyUH+3OYIgGBgEwZNBELwXBME7QRBcvPXrvw6C4OMgCF7f+u+4HfhdbmORaCsb02oflL+NPk7dxpzfU9b2bf0Zt7FItKWNQHQFQHv/AyqBhcDeQBXwBjCsEH97B9rWHzhg6/+7AvOAYcCvgf/lNu48NqbZvp3BRh+nbuPOYp/bWD426l+hlKmDgAVhGH4QhuEXwD3ASQX629slDMNPwjCcvfX/64H3gNpW/Cq3sYi0kY2ptQ/K30Yfpy2i3G0sd/vAbSwqbWgjULhjvlpgSeLzpeTR6PYiCII9gf2Bl7d+6aIgCN4MguC2IAh6NPPjbmNKyMPGkrAPyt9GH6c7vY3lbh+4jakhTxuBwm2mmroBM1VphEEQ7AJMA34ahuE64P8B+wCjgU+A/9vcr2jia25jgcnTxtTbB+Vvo49Tt5Hytw/cxlTQBjYChdtMLQUGJj7/CrCsQH+7WYIg6Ej0Zv53GIYPAIRhuCIMw0wYhlngz0Ry5fZwG4tMG9iYavug/G30ceo2bqXc7QO3sei0kY1A4TZTrwKDgiDYKwiCKuB04KEC/e3tEgRBAPwVeC8Mw+sSX++feNnJwNvN/Cq3sYi0kY2ptQ/K30Yfp4bbWP72gdtYVNrQxoiWRqy39h9wHFG0/ELg0kL93R1o1zeIZMc3gde3/jsOuBN4a+vXHwL6u43lb2Na7dsZbPRx6jbuTPa5jeVjYxiGXgHdcRzHcRwnH7wCuuM4juM4Th74ZspxHMdxHCcPfDPlOI7jOI6TB76ZchzHcRzHyQPfTDmO4ziO4+SBb6Ycx3Ecx3HywDdTjuM4juM4eeCbKcdxHMdxnDz4/1/HWr1UoQ0lAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x180 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x180 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x180 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x180 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x180 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x180 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x180 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(10):\n",
    "\n",
    "    ##########################\n",
    "    ### RANDOM SAMPLE\n",
    "    ##########################    \n",
    "    \n",
    "    n_images = 10\n",
    "    rand_features = torch.randn(n_images, num_latent).to(device)\n",
    "    new_images = model.decoder(rand_features)\n",
    "\n",
    "    ##########################\n",
    "    ### VISUALIZATION\n",
    "    ##########################\n",
    "\n",
    "    image_width = 28\n",
    "\n",
    "    fig, axes = plt.subplots(nrows=1, ncols=n_images, figsize=(10, 2.5), sharey=True)\n",
    "    decoded_images = new_images[:n_images]\n",
    "\n",
    "    for ax, img in zip(axes, decoded_images):\n",
    "        curr_img = img.detach().to(torch.device('cpu'))\n",
    "        ax.imshow(curr_img.view((image_width, image_width)), cmap='binary')\n",
    "        \n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "numpy       1.15.4\n",
      "torch       1.0.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%watermark -iv"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
  },
  "toc": {
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
